Prelims
a) R1C12 = {17/26/35}, no 4,8,9
b) R23C1 = {39/48/57}, no 1,2,6
c) R34C9 = {19/28/37/46}, no 5
d) R4C45 = {89}
e) R4C78 = {14/23}
f) R5C89 = {29/38/47/56}, no 1
g) R7C45 = {39/48/57}, no 1,2,6
h) R78C6 = {19/28/37/46}, no 5
i) R8C45 = {14/23}
j) 23(3) cage at R6C8 = {689}
k) 11(3) cage at R8C3 = {128/137/146/236/245}, no 9
l) 14(4) cage at R1C7 = {1238/1247/1256/1346/2345}, no 9
m) 36(8) cage at R2C2 = {12345678}, no 9
Steps resulting from Prelims and Initial Placements.
1a. Naked pair {89} in R4C45, locked for R4 and N5, clean-up: no 1,2 in R3C9
1b. Naked triple {689} in 23(3) cage at R6C8, CPE no 6,8,9 in R5C8, clean-up: no 2,3,5 in R5C9
1c. 45 rule on C1 1 innie R1C1 = 1 -> R1C2 = 7, clean-up: no 5 in R23C1
1d. 45 rule on N69 1 innie R4C9 = 1 -> R3C9 = 9, clean-up: no 3 in R2C1, no 4 in R4C78
1e. Naked pair {23} in R4C78, locked for R4 and N6, clean-up: no 8 in R5C9
1f. 36(8) cage at R2C2 = {12345678}, 7 in R6C345, locked for R6
1g. 7 in N6 only in R5C789, locked for R5
1h. 23(3) cage at R6C8 = {689}, 9 locked for C8
2. 45 rule on N145 1 outie R3C4 = 1 innie R4C6, R4C6 = {4567} -> R3C4 = {4567}
3. 45 rule on N3 1 remaining innie R3C7 = 1 outie R2C6 + 6 -> R2C6 = {12}, R3C7 = {78}
3a. Min R3C7 + R4C6 = 11 -> max R3C6 = 5
4a. 32(7) cage at R1C3 must contain 1 in R5C34, locked for R5
4b. 36(8) cage at R2C2 must contain 1 in R6C2345, locked for R6
4c. 14(3) cage at R5C5 = {356} (only remaining combination), locked for N5, clean-up: no 5,6 in R3C4 (step 2)
4d. R5C89 = {47} (cannot be [56] which clashes with 14(3) cage, ALS block), locked for R5 and N6
4e. 5,6 in R4 only in R4C123, locked for N4
4f. 5 in N6 only in R56C7, locked for C7
4g. 32(7) cage must contain 3 in R1235C3, locked for C3
5a. 17(3) cage at R1C4 = {269/359/368/458}
5b. 18(3) cage at R2C4 = {279/369/378/459/468} (cannot be {189/567} which clash with 17(3) cage), no 1
5c. 1 in N2 only in R23C6, locked for C6, clean-up: no 9 in R78C6
5d. 45 rule on N2 3 innies R2C6 + R3C46 = 10 contains 1 = {127/145}, no 3
5e. 5 of {145} must be in R3C6 -> no 4 in R3C6
5f. 2 of {127} must be in R2C6 (cannot be [172] which clashes with R2C6 + R3C7 = [17], step 3), no 2 in R3C6
5g. 45 rule on N23 3 remaining innies R3C467 = 16 = [457/718], 7 locked for R3
6. R78C6 = {28/37/46}, R8C45 = {14/23} -> combined cage R78C6 + R8C45 = {28}{14}/{37}{14}/{46}{23}, 4 locked for N8, clean-up: no 8 in R7C45
6a. R78C6 = {28/46} (cannot be {37} which clashes with R7C45), no 3,7
6b. Killer pair 2,4 in R78C6 and R8C24, locked for N8
6c. 18(3) cage at R9C4 = {189/369/567} (cannot be {378} which clashes with R7C45)
6d. 15(3) cage at R9C7 = {249/258/267/348/357/456} (cannot be {159/168} which clash with 18(3) cage), no 1
6e. 45 rule on C789 3 outies R234C6 = 10 = [217/154]
6f. Killer pair 2,4 in R234C6 and R78C6, locked for C6
7. 21(4) cage at R5C7 must contain 5 = {1569/2568/3459/3567} (cannot be {1578} which clashes with R3C7)
8. 45 rule on C6789 2 innies R19C6 = 1 outie R5C5 + 11
8a. Min R5C5 = 3 -> min R19C6 = 14, no 3 in R19C6
8b. 3 in C6 only in R56C6, locked for N5
8c. Min R5C5 = 5 -> min R19C6 = 16, no 5,6 in R19C6
9. 32(7) cage at R1C3 and 36(8) cage at R2C2 must both contain 3, locked for N14 (caged X-Wing), clean-up: no 9 in R2C1
9a. Naked pair {48} in R23C1, locked for C1 and N1
9b. Naked pair {29} in R56C1, locked for C1 and N4, R4C1 = 5 (cage sum)
9c. Naked triple {367} in 16(3) cage at R7C1, locked for N7
9d. 36(8) cage = {12345678}, 8 locked for N4
9e. 32(7) cage R1C3 = {1234679} (only remaining combination), no 5, 9 locked for C3
9f. 5 in N1 only in R23C2, locked for C2
9g. 4 in R6 only in R6C2345, locked for 36(8) cage -> R4C2 = 6
10. Killer pair 4,8 in R3C1 and R3C467 (step 5g), locked for R3
[That’s how I saw it although, after going through Ed’s walkthrough I can see that it’s actually naked triple {478} in R3C147.]
10a. 18(3) cage at R2C4 (step 5b) = {279/369/378/459} (cannot be {468} = {48}6 which clashes with R2C1)
10b. 2 of {279} must be in R3C5 -> no 2 in R2C45
10c. 17(3) cage at R1C4 (step 5a) = {269/368/458} (cannot be {359} which clashes with 18(3) cage)
11a. 18(3) cage at R7C2 = {189/459}, no 2
11b. 5 on {459} must be in R7C3 -> no 4 in R7C3
11c. 45 rule on R9 1 innie R9C1 = 1 outie R8C3 + 1 -> R8C3 = {25}, R9C1 = {36}
11d. 18(3) cage at R9C4 (step 6c) = {189/567} (cannot be {369} which clashes with R9C1), no 3
11e. Hidden killer pair 7,9 in 18(3) cage and 15(3) cage at R9C7 (step 6d) for R9, 18(3) cage contains one of 7,9 -> 15(3) cage must contain one of 7,9 = {249/267/357} (cannot be {258/348/456}, no 8
11f. 9 of {249} must be in R9C7 -> no 4 in R9C7
11g. 14(3) cage at R7C9 = {158/167/248/356} (cannot be {257/347} which clash with 15(3) cage at R9C7)
11h. 45 rule on N9 3 innies R7C78 + R8C7 = 16 = {169/349/367} (cannot be {178} because 21(4) cage at R5C7 (step 7) doesn’t contain both of 1,7, cannot be {268} which clashes with 14(3) cage), no 2,8
11i. 8 in N9 only in 14(3) cage = {158/248}, no 3,6,7
11j. 1 of {158} must be in R8C8 -> no 5 in R8C8
11k. 23(3) cage at R6C8 = {689}, 8 locked for R6 and N6
11l. R5C2 = 8 (hidden single in N4)
12. 15(3) cage at R9C7 (step 11e) = {249/267/357}
12a. Consider combinations for 14(3) cage at R7C9 (step 11i) = {158/248}
14(3) cage = {158} => R8C8 = 1, naked pair {58} in R78C9, locked for C9, R6C9 = 6, R67C8 = [89] => 15(3) cage = {267}
or 14(3) cage = {248}, 2 locked for N9 -> 15(3) cage = {357}
-> 15(3) cage = {267/357}, no 4,9, 7 locked for R9 and N9
[Cracked. The rest is fairly straightforward.]
12b. Naked pair {89} in R19C6, locked for C6, clean-up: no 2 in R78C6
12c. Naked pair {46} in R78C6, locked for C6 and N8, clean-up: no 1 in R8C45
12d. Naked pair {35} in R56C6, 5 locked for C6 and N5 -> R5C5 = 6
12e. Naked pair {23} in R8C45, locked for R8 and N8, clean-up: no 9 in R7C45
12f. Naked pair {57} in R7C45, locked for R7 and N8
12g. R234C6 = [217], R3C7 = 8, R23C1 = [84], R3C4 = 7, R4C3 = 4, R7C45 = [57]
12h. R8C3 = 5 -> R9C24 = 6 = [42]
12i. Naked triple {369} in R123C3, 3 locked for C3 and N1
13a. 15(3) cage at R7C9 = {357} (only remaining combination), 3 locked for R9 and N9
13b. R7C9 = 2 (hidden single in N9) -> R8C89 = 12 = {48}, locked for R8, 4 locked for N9
13c. 4 in C7 only in R12C7, locked for N3
13d. Naked quad {1569} in 21(4) cage at R5C7, locked for C7
14. 18(3) cage at R2C4 (step 5b) = {369/459}, 9 locked for R2 and N2
15a. R2C8 = 1 (hidden single in N3)
15b. 7 in R2 only in R2C79 -> 16(4) disjoint cage at R1C9 = {2347} -> R1C9 = 3
15c. R1C6 = 8 -> R1C45 = 9 = [45]
and the rest is naked singles.